Fill in the blank correctly

1. Dr. __________ wrote the Cat in the Hat.

2. ___________ is the third planet from the sun.

3. There are _________ hours in a day.

Fill in the blank correctly

1. Dr. Seuss wrote the Cat in the Hat.

2. Earth is the third planet from the sun.

3. There are 24 hours in a day.

Fill in the blank is like solving an equation

Fill in the blank

• Earth is the third planet from the Sun.

• Only one word makes this sentence true

Equations

• 3x = 15

• Only one value of x make this equation true.

• How can we “find x”?

Equations

• Equations are balanced

• Left hand side equals the right hand side

• 3x = 15

56 = 8•7

1.2 Solving One Step Equations

• Variables are grouchy – they like to be alone!

• Solve – means find what number the variable is equal to.

• Isolate variable by performing the INVERSE OPERATION to both sides of equation

• Inverse operations “UNDO” what has been done to the variable.

1.2 Solving One Step Equations

Operation Inverse Operation

Addition Subtraction

Subtraction Addition

Multiplication Division

Division Multiplication

ONE STEP EQUATIONSExample 1 Solve x + 4 = 12

What is the variable?

Using the subtraction property of equality, subtract 4 from both sides of the equation.

- 4

x

x + 4 = 12

The variable is x.

Addition.

Subtraction.What is the inverse operation (the one that will undo what is being done to the variable)?

What operation is being performed on the variable?

- 4

8=

The subtraction property of equality tells us to subtract the same thing on both sides to keep the equation equal.

ONE STEP EQUATIONSExample 2 Solve y - 7 = -13

What is the variable?

Using the addition property of equality, add 7 to both sides of the equation.

y - 7 = -13

+ 7

y

The variable is y.

Subtraction.

Addition.

What operation is being performed on the variable?

What is the inverse operation (the one that will undo what is being done to the variable)?

+ 7

= -6

The addition property of equality tells us to add the same thing on both sides to keep the equation equal.

ONE STEP EQUATIONSExample 3 Solve –6a = 12

What is the variable?

Using the division property of equality, divide both sides of the equation by –6.

–6a = 12

-6

a

The variable is a.

What operation is being performed on the variable? Multiplication.

What is the inverse operation (the one that will undo what is being done to the variable)? Division

-6

= -2

The division property of equality tells us to divide the same thing on both sides to keep the equation equal.

ONE STEP EQUATIONSExample 4 Solve

2b

What is the variable?

Using the multiplication property of equality, multiply both sides of the equation by 2.

= -102b

2b

b

The variable is b.What operation is being performed on the variable? Division. What is the inverse operation (the one that will undo what is being done to the variable)? Multiplication

= -102 • • 2

= -20

= -10

The multiplication property of equality tells us to multiply the same thing on both sides to keep the equation equal.

210

3y 3

2

3

2

10 3

1 2y

Multiply both sides by the reciprocal of the fraction.

cancel out t .3 2

2 3o 1

210

3y

Multiply the numerators. Multiply the denominators.30

2y Simplify15

Additional Example 1A: Solving One-Step Equations with Decimals

Solve the equation. Check your answer.

k – 6.2 = 9.5

k – 6.2 = 9.5 6.2 is subtracted from k.

Add 6.2 to both sides to undo the subtraction.

+ 6.2 + 6.2

k = 15.7

Check

k – 6.2 = 9.5Substitute 15.7 for k in the equation.15.7 – 6.2 = 9.5

?

9.5 = 9.5?

15.7 is the solution.

Check It Out: Example 1A

Solve the equation. Check your answer.

n – 3.7 = 8.6

n – 3.7 = 8.6 3.7 is subtracted from n.

Add 3.7 to both sides to undo the subtraction.

+ 3.7 + 3.7

n = 12.3

Check

n – 3.7 = 8.6Substitute 12.3 for n in the equation.12.3 – 3.7 = 8.6

?

8.6 = 8.6?

12.3 is the solution.

Additional Example 1B: Solving One-Step Equations with Decimals

Solve the equation. Check your answer.

6k = 7.2

6k = 7.2

k is multiplied by 6.

Divide both sides by 6 to undo the multiplication.

k = 1.2

Check

6k = 7.2Substitute 1.2 for k in the equation.6(1.2) = 7.2

?

7.2 = 7.2?

1.2 is the solution.

6 6

6k = 7.2

Additional Example 1C: Solving One-Step Equations with Decimals

Solve the equation. Check your answer.

= 0.6

= 0.6

m is divided by 7.

Multiply both sides by 7 to undo the division.

m = 4.2

Check

Substitute 4.2 for m in the equation.

0.6 = 0.6?

4.2 is the solution.

· 7

m7

m7

· 7

= 0.6m7

= 0.64.27

?